To be honest the whole approach always felt like some form of corruption/kick back to me. You give an incentive to the employee that is dissociated from the interest of their employer.
There’s indirect benefits to the business as well since they’ll be first to be put on a flight after cancellations, can get guaranteed lodging in areas that sell out often, and can use their points to upgrade making their trip nicer.
So it’s unwise to chase that as an employer. Let them get points and be comfortable and use them to take the family somewhere.
Is this a thing for most people?
Being in an unfamiliar place is one of my greatest joys. I am never more relaxed than my first day in a new city where I know absolutely nothing, and turning each new corner is a revelation.
This is mitigated by the employer setting rates, per-diem, rules on what seats you can purchase, etc. and the employer can't use the points from the frequent flyer program anyway. If there's, say, a $50 fare difference and that causes an employee to choose a more expensive flight (because the comparable flights are comparable) because they get points it's fine and basically an added benefit. In consulting for example that's a stated benefit in employee handbooks.
Of course that's not to say employees of companies can't go against the interest of their employer here, but it's up to the employer to set guidelines and for the employee to follow them.
This isn't always true. Some employers insist you book through their internal travel department or use their corporate FF accounts, which kick all the mileage and hotel night benefits to them. It's not common, fortunately, but it does happen.